[en] In this study we fabricated lateral superlattices (LSLs) based on the selectively doped GaAs/AlAs heterostructures with a high-mobility two-dimensional (2D) electron gas. The LSLs were formed using the electron-beam lithography and lift-off techniques, which produced a set of metallic strips on top of a heterojunction. The amplitude of the 2D electron gas modulation in the LSL was controlled by the gate voltage applied to the metallic strips. The LSLs with two different periods (a = 200 nm and 500 nm) were used to investigate the influence of microwave radiation with the frequency of 110–150 GHz on the 2D electron transport at the temperature T = 1.6 K in the magnetic field B < 1 T. We have found that zero-resistance states (ZRSs) appear under the microwave radiation in the 2D systems with a unidirectional periodic modulation. These ZRSs are located at the minima of commensurability oscillations